The US, Britain and France are scrambling to retain their influence with Syrian opposition groups amid fears that most support from the Gulf states has been diverted towards extremist Islamic groups.

Rising concern that an increasingly sectarian civil war could spread across the region, combined with reports of brutality by some opposition groups, and evidence that the best-organised and best-funded rebel groups are disproportionately Salafist (militant Sunni fundamentalists), has triggered an urgent policy change in western capitals.

Washington, London and Paris now agree that efforts to encourage a unified opposition around the exile-led Syrian National Council (SNC) have failed, and are now seeking to cultivate more direct links with internal Syrian groups.

Ausama Monajed, a British-based SNC member, conceded: "The SNC could have done a better job, a more effective job, in organising the forms on the ground, and now the key issue is to bring fighting groups together in some other framework. But that does not mean that the SNC will be sidelined altogether. It is still the biggest political grouping and has a political and diplomatic role to play."

Hillary Clinton, the US secretary of state, flew to Istanbul on Saturday to meet Syrian opposition activists and boost military and intelligence co-operation with the Turkish government to prevent the violence spreading across the border. Jon Wilks, Britain's special envoy to the Syrian opposition, was also in Istanbul last week for a meeting with someone the Foreign Office described as "a senior political representative" of the Free Syrian Army (FSA), during which he stressed the importance of human rights and respect for minorities as a condition of future co-operation.

On Friday, the UK announced £5m in new non-military aid to Syrian opposition groups, pointedly insisting that all the recipients should be organisations inside Syria, therefore excluding the SNC. Clinton's meetings in Istanbul were also intended to sidestep the exile group, on the grounds that it had little influence on events inside Syria.

"This was a conclusion the state department came to some time ago, and it is just now percolating through into policy," said Joseph Holliday, an expert on the Syrian rebels at the Washington-based Institute for the Study of War.

Both Wilks and the US ambassador to Syria, Robert Ford – who was withdrawn from Damascus last October out of concern for his safety – took part in an unpublicised meeting in Cairo at the beginning of the month. The aim of the meeting, organised by the Doha centre of the Washington-based Brookings Institution thinktank, and attended by external and internal opposition groups including the FSA, was to set up a broad-based committee to hammer out a mutually agreed transition plan.

In France, the government of François Hollande is under intense pressure, particularly from former president Nicolas Sarkozy, to intervene directly on the side of the opposition.

Fabrice Balanche, a Syria expert at the University of Lyon, said the incoming foreign minister, Laurent Fabius, "realised that France had invested too much political capital in the SNC". He said the new government had instead thrown its weight behind Manaf Tlass – a former Republican Guard general and member of Bashar al-Assad's inner circle – who defected in July. France is hoping the FSA will coalesce around Tlass, providing some coherence to the disparate array of militias.

However, a Syrian financier linked to the opposition warned that the FSA would remain divided as long as it relied on multiple, uncoordinated sources of funding. "The local brigade commanders on the ground swear allegiance to whoever supports them and the expat community sending them money is completely divided," the financier said. "These are [Syrian] expats in the States and the Gulf using their own trusted channels for getting money through, so the money is pouring in from many different pockets. The number of fighters each commander can summon wax and wane with his ability to arm and pay them and their families, so there is no particular leader with enough clout to bring the brigades together."

The exceptions to this rule, he said, were Saudi Arabia and Qatar, but that money went disproportionately to Salafist and jihadist groups. "The most organised systems are run by extreme Islamist groups and they have the highest income. The more extreme brutality tends to come from that direction, but they have the most ammunition and guns, and they get their money from a unified source. All the other money comes from multiple sources and multiple channels. You can only unify these units with a unified source of money."

Julien Barnes-Dacey, a Middle Eastern expert at the European Council for Foreign Relations, said that western states realised that "if they don't get on board now, they will lose every opportunity of leverage. If the Saudis and Qataris run loose with the groups they are backing, there will be great chance of blowback."

"Blowback" is a term widely used to describe the backing of jihadist rebels against the Soviet army in Afghanistan in the 1980s, which provided a recruiting ground for al-Qaida and global jihadism.

According to western diplomats, a Kuwaiti sheikh is also playing a key role in channelling money collected in the Gulf to militant groups judged to have sufficient Salafist credentials.

Western influence with the FSA is limited by a continued refusal to supply arms because of the uncertainty of where the weapons would end up. Barack Obama is reported to have issued a "presidential finding" (a secret executive order) earlier this year, stepping up CIA activity in and around Syria, but that too stopped short of arms supplies.

According to reports from Washington and the Turkish-Syrian border, the main US intelligence role as been to act with the Turks in stopping arms reaching groups they view as undesirable.

On her visit to Istanbul, Clinton did hint at more direct action in the future. She said the US and Turkey had agreed on "very intensive operational planning" by military and intelligence officials. "We have been closely co-ordinating over the course of this conflict, but now we need to get into the real details."

Clinton did not exclude the possibility of setting up a no-fly zone, long advocated by Turkey but rejected up to now by Washington because it would require a large-scale military operation.

On Saturday she said the joint US-Turkish planning team would perform an "intense analysis" of all options as a possible precursor to more direct assistance.